SLATEC Routines --- EISDOC ---
*DECK EISDOC
SUBROUTINE EISDOC
C***BEGIN PROLOGUE EISDOC
C***PURPOSE Documentation for EISPACK, a collection of subprograms for
C solving matrix eigen-problems.
C***LIBRARY SLATEC (EISPACK)
C***CATEGORY D4, Z
C***TYPE ALL (EISDOC-A)
C***KEYWORDS EIGENVALUES, EIGENVECTORS, EISPACK
C***AUTHOR Vandevender, W. H., (SNLA)
C***DESCRIPTION
C
C **********EISPACK Routines**********
C
C single double complx
C ------ ------ ------
C
C RS - CH Computes eigenvalues and, optionally,
C eigenvectors of real symmetric
C (complex Hermitian) matrix.
C
C RSP - - Compute eigenvalues and, optionally,
C eigenvectors of real symmetric matrix
C packed into a one dimensional array.
C
C RG - CG Computes eigenvalues and, optionally,
C eigenvectors of a real (complex) general
C matrix.
C
C BISECT - - Compute eigenvalues of symmetric tridiagonal
C matrix given interval using Sturm sequencing.
C
C IMTQL1 - - Computes eigenvalues of symmetric tridiagonal
C matrix implicit QL method.
C
C IMTQL2 - - Computes eigenvalues and eigenvectors of
C symmetric tridiagonal matrix using
C implicit QL method.
C
C IMTQLV - - Computes eigenvalues of symmetric tridiagonal
C matrix by the implicit QL method.
C Eigenvectors may be computed later.
C
C RATQR - - Computes largest or smallest eigenvalues
C of symmetric tridiagonal matrix using
C rational QR method with Newton correction.
C
C RST - - Compute eigenvalues and, optionally,
C eigenvectors of real symmetric tridiagonal
C matrix.
C
C RT - - Compute eigenvalues and eigenvectors of
C a special real tridiagonal matrix.
C
C TQL1 - - Compute eigenvalues of symmetric tridiagonal
C matrix by QL method.
C
C TQL2 - - Compute eigenvalues and eigenvectors
C of symmetric tridiagonal matrix.
C
C TQLRAT - - Computes eigenvalues of symmetric
C tridiagonal matrix a rational variant
C of the QL method.
C
C TRIDIB - - Computes eigenvalues of symmetric
C tridiagonal matrix given interval using
C Sturm sequencing.
C
C TSTURM - - Computes eigenvalues of symmetric tridiagonal
C matrix given interval and eigenvectors
C by Sturm sequencing. This subroutine
C is a translation of the ALGOL procedure
C TRISTURM by Peters and Wilkinson. HANDBOOK
C FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA,
C 418-439(1971).
C
C BQR - - Computes some of the eigenvalues of a real
C symmetric matrix using the QR method with
C shifts of origin.
C
C RSB - - Computes eigenvalues and, optionally,
C eigenvectors of symmetric band matrix.
C
C RSG - - Computes eigenvalues and, optionally,
C eigenvectors of symmetric generalized
C eigenproblem: A*X=(LAMBDA)*B*X
C
C RSGAB - - Computes eigenvalues and, optionally,
C eigenvectors of symmetric generalized
C eigenproblem: A*B*X=(LAMBDA)*X
C
C RSGBA - - Computes eigenvalues and, optionally,
C eigenvectors of symmetric generalized
C eigenproblem: B*A*X=(LAMBDA)*X
C
C RGG - - Computes eigenvalues and eigenvectors
C for real generalized eigenproblem:
C A*X=(LAMBDA)*B*X.
C
C BALANC - CBAL Balances a general real (complex)
C matrix and isolates eigenvalues whenever
C possible.
C
C BANDR - - Reduces real symmetric band matrix
C to symmetric tridiagonal matrix and,
C optionally, accumulates orthogonal similarity
C transformations.
C
C HTRID3 - - Reduces complex Hermitian (packed) matrix
C to real symmetric tridiagonal matrix by unitary
C similarity transformations.
C
C HTRIDI - - Reduces complex Hermitian matrix to real
C symmetric tridiagonal matrix using unitary
C similarity transformations.
C
C TRED1 - - Reduce real symmetric matrix to symmetric
C tridiagonal matrix using orthogonal
C similarity transformations.
C
C TRED2 - - Reduce real symmetric matrix to symmetric
C tridiagonal matrix using and accumulating
C orthogonal transformations.
C
C TRED3 - - Reduce symmetric matrix stored in packed
C form to symmetric tridiagonal matrix using
C orthogonal transformations.
C
C ELMHES - COMHES Reduces real (complex) general matrix to
C upper Hessenberg form using stabilized
C elementary similarity transformations.
C
C ORTHES - CORTH Reduces real (complex) general matrix to upper
C Hessenberg form orthogonal (unitary)
C similarity transformations.
C
C QZHES - - The first step of the QZ algorithm for solving
C generalized matrix eigenproblems. Accepts
C a pair of real general matrices and reduces
C one of them to upper Hessenberg and the other
C to upper triangular form using orthogonal
C transformations. Usually followed by QZIT,
C QZVAL, QZ
C
C QZIT - - The second step of the QZ algorithm for
C generalized eigenproblems. Accepts an upper
C Hessenberg and an upper triangular matrix
C and reduces the former to quasi-triangular
C form while preserving the form of the latter.
C Usually preceded by QZHES and followed by QZVAL
C and QZVEC.
C
C FIGI - - Transforms certain real non-symmetric
C tridiagonal matrix to symmetric tridiagonal
C matrix.
C
C FIGI2 - - Transforms certain real non-symmetric
C tridiagonal matrix to symmetric tridiagonal
C matrix.
C
C REDUC - - Reduces generalized symmetric eigenproblem
C A*X=(LAMBDA)*B*X, to standard symmetric
C eigenproblem using Cholesky factorization.
C
C REDUC2 - - Reduces certain generalized symmetric
C eigenproblems standard symmetric eigenproblem,
C using Cholesky factorization.
C
C - - COMLR Computes eigenvalues of a complex upper
C Hessenberg matrix using the modified LR method.
C
C - - COMLR2 Computes eigenvalues and eigenvectors of
C complex upper Hessenberg matrix using
C modified LR method.
C
C HQR - COMQR Computes eigenvalues of a real (complex)
C upper Hessenberg matrix using the QR method.
C
C HQR2 - COMQR2 Computes eigenvalues and eigenvectors of
C real (complex) upper Hessenberg matrix
C using QR method.
C
C INVIT - CINVIT Computes eigenvectors of real (complex)
C Hessenberg matrix associated with specified
C eigenvalues by inverse iteration.
C
C QZVAL - - The third step of the QZ algorithm for
C generalized eigenproblems. Accepts a pair
C of real matrices, one quasi-triangular form
C and the other in upper triangular form and
C computes the eigenvalues of the associated
C eigenproblem. Usually preceded by QZHES,
C QZIT, and followed by QZVEC.
C
C BANDV - - Forms eigenvectors of real symmetric band
C matrix associated with a set of ordered
C approximate eigenvalue by inverse iteration.
C
C QZVEC - - The optional fourth step of the QZ algorithm
C for generalized eigenproblems. Accepts
C a matrix in quasi-triangular form and another
C in upper triangular and computes the
C eigenvectors of the triangular problem
C and transforms them back to the original
C coordinates Usually preceded by QZHES, QZIT,
C QZVAL.
C
C TINVIT - - Eigenvectors of symmetric tridiagonal
C matrix corresponding to some specified
C eigenvalues, using inverse iteration.
C
C BAKVEC - - Forms eigenvectors of certain real
C non-symmetric tridiagonal matrix from
C symmetric tridiagonal matrix output from FIGI.
C
C BALBAK - CBABK2 Forms eigenvectors of real (complex) general
C matrix from eigenvectors of matrix output
C from BALANC (CBAL).
C
C ELMBAK - COMBAK Forms eigenvectors of real (complex) general
C matrix from eigenvectors of upper Hessenberg
C matrix output from ELMHES (COMHES).
C
C ELTRAN - - Accumulates the stabilized elementary
C similarity transformations used in the
C reduction of a real general matrix to upper
C Hessenberg form by ELMHES.
C
C HTRIB3 - - Computes eigenvectors of complex Hermitian
C matrix from eigenvectors of real symmetric
C tridiagonal matrix output from HTRID3.
C
C HTRIBK - - Forms eigenvectors of complex Hermitian
C matrix from eigenvectors of real symmetric
C tridiagonal matrix output from HTRIDI.
C
C ORTBAK - CORTB Forms eigenvectors of general real (complex)
C matrix from eigenvectors of upper Hessenberg
C matrix output from ORTHES (CORTH).
C
C ORTRAN - - Accumulates orthogonal similarity
C transformations in reduction of real general
C matrix by ORTHES.
C
C REBAK - - Forms eigenvectors of generalized symmetric
C eigensystem from eigenvectors of derived
C matrix output from REDUC or REDUC2.
C
C REBAKB - - Forms eigenvectors of generalized symmetric
C eigensystem from eigenvectors of derived
C matrix output from REDUC2
C
C TRBAK1 - - Forms the eigenvectors of real symmetric
C matrix from eigenvectors of symmetric
C tridiagonal matrix formed by TRED1.
C
C TRBAK3 - - Forms eigenvectors of real symmetric matrix
C from the eigenvectors of symmetric tridiagonal
C matrix formed by TRED3.
C
C MINFIT - - Compute Singular Value Decomposition
C of rectangular matrix and solve related
C Linear Least Squares problem.
C
C***REFERENCES B. T. Smith, J. M. Boyle, J. J. Dongarra, B. S. Garbow,
C Y. Ikebe, V. C. Klema and C. B. Moler, Matrix Eigen-
C system Routines - EISPACK Guide, Springer-Verlag,
C 1976.
C***ROUTINES CALLED (NONE)
C***REVISION HISTORY (YYMMDD)
C 811101 DATE WRITTEN
C 861211 REVISION DATE from Version 3.2
C 891214 Prologue converted to Version 4.0 format. (BAB)
C 900723 PURPOSE section revised. (WRB)
C 920501 Reformatted the REFERENCES section. (WRB)
C***END PROLOGUE EISDOC